# Question about stress - strain graph and definition of hardness

• B
• songoku
In summary, the conversation discusses the definitions of ultimate tensile strength, fracture stress, and hardness in materials. Point D represents the ultimate tensile strength, which is the highest possible stress a material can withstand. Point E is the fracture stress, which is the stress at which the material breaks. The conversation also talks about the resistance to plastic deformation and scratching, which are components of hardness. The example of sponge as a hard material is questioned, but the teacher may have had a specific reason for using it.
songoku
TL;DR Summary

This is from my notes:

Point D is called ultimate tensile strength and defined as highest possible within this material.
So it means that point D should be at the highest point of the graph (more like absolute maximum in math)? Because it seems that from the graph point D is not at maximum point, or maybe point D is a little bit misplaced?Point E is fracture stress, defined as value of stress in the material when sample breaks.
From the graph, point E is below point D so the amount of stress needed to break the material is less than the highest stress (ultimate tensile strength) the material can withstand? Does it mean that the fracture point actually depends more on the strain rather than stress? Because I find it a bit weird that the material can withstand, let say 106 Pa, of stress but fracture by 105 Pa of stress.Last question is about definition of hardness (not related to the graph). Definition of hardness in my note is the resistance to plastic deformation of the surface or resistance to scratching.
What does it mean by "resistance to plastic deformation of the surface"? Does it mean that we only consider the surface of the material, whether it can undergo plastic deformation or not, or maybe the surface is resistance to scratching or not?
One example of the material given by the teacher is sponge. I can imagine sponge is resistance to plastic deformation but I don't understand the "of the surface" part because if I squeeze a sponge, all parts of the material deform, not only the surface. I am also not sure about the resistance of scratching of sponge. I think maybe I can leave some scratch on its surface by using knife.

Thanks

Delta2
Lnewqban said:
I think I get the answer to my question but I just want to confirm my understanding, is it correct to say that sponge is wrong example of material that is hard (having high hardness)?

Thanks

I am sure your teacher had a good reason to use that example.
Unless a specific natural sponge has some hard horns or shell, it seems to me that it is mostly “not hard”.

songoku
Thank you very much Lnewqban

Lnewqban

## 1. What is a stress-strain graph?

A stress-strain graph is a graphical representation of the relationship between the amount of force (stress) applied to a material and the resulting deformation (strain) of the material. It is used to determine the mechanical properties of a material, such as its elasticity and strength.

## 2. How is a stress-strain graph created?

A stress-strain graph is created by subjecting a material to increasing amounts of force and measuring the resulting strain. The data is then plotted on a graph with stress on the y-axis and strain on the x-axis. The slope of the resulting curve represents the material's stiffness, while the area under the curve represents its toughness.

## 3. What is the definition of hardness in relation to a stress-strain graph?

Hardness is the ability of a material to resist permanent deformation when subjected to a force. In a stress-strain graph, hardness is represented by the steepness of the initial linear portion of the curve, known as the elastic region. A steeper curve indicates a harder material, as it requires more force to cause a given amount of deformation.

## 4. How is the yield strength of a material determined from a stress-strain graph?

The yield strength of a material is determined by finding the point on the stress-strain curve where the material transitions from the linear elastic region to the plastic region. This point is known as the yield point, and the corresponding stress is the yield strength of the material.

## 5. What is the difference between ductility and brittleness in a stress-strain graph?

Ductility is the ability of a material to deform plastically before fracturing, while brittleness is the tendency of a material to fracture without significant plastic deformation. In a stress-strain graph, a material with a longer, flatter curve represents higher ductility, while a material with a shorter, steeper curve represents higher brittleness.

• Introductory Physics Homework Help
Replies
9
Views
3K
• Introductory Physics Homework Help
Replies
4
Views
293
• Classical Physics
Replies
5
Views
1K
• Engineering and Comp Sci Homework Help
Replies
3
Views
1K
• Mechanical Engineering
Replies
2
Views
4K
• Mechanical Engineering
Replies
6
Views
1K
• Introductory Physics Homework Help
Replies
1
Views
2K
• Mechanical Engineering
Replies
1
Views
934
• Classical Physics
Replies
2
Views
992
• Mechanical Engineering
Replies
5
Views
817